We refer the reader to [1]} and [2]} for the definition of a restricted Lie algebra,
and for the construction of the \([p]\) -mapping on a given Lie algebra
(\(\mathfrak {m}_2(p)\)  in the current paper) used below. For any \(j\ge 2\)  and
\(g_1,\dots , g_j\in \mathfrak {m}_2(p)\) , we denote the \(j\) -fold bracket
\([g_1,g_2,g_3,\dots , g_j]=[[\dots [[g_1,g_2],g_3],\dots ],g_j].\) 
